Tetration/Code/HolomorphicBaseSqrt2v01

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// Generator of the eps version of plot ot holomorphic tetration at base
HolomorphicTetrationBaseSqrt2v01.jpg
in the compex plane

// The following graphical functions are required to compile it:
// ContourPlot/code/ado.cin
// ContourPlot/code/conto.cin
// Copyleft 2008,2009 by Dmitrii Kouznetsov

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex.h>
#define z_type complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
                                                                                                                                          
DB coef[12]= // Copypast from Mathematica
{2.00000000000000000, -1.00000000000000000, -0.564722838317732364,
-0.338177586851183300, -0.210331302138627770, -0.134454879052109797,
-0.0877843886012191373, -0.0582880930830946915, -0.0392407117837278383,
-0.0267232860342981439, -0.0183765205976375959, -0.0127420898467766479};
                                                                                                                                          
z_type sqrt2a(z_type z){int n; z_type e,s;
                       e=exp(-0.36651292058166432701*(z+1.25155147882219));
                       s=coef[11];
                       for(n=10;n>=0;n--) { s*=e; s+=coef[n]; }
                       return s;
                       }
                                                                                                                                          
z_type sqrt2b(z_type z){ if(Re(z)>5) return sqrt2a(z);
                       return log(sqrt2b(z+1.))/log(sqrt(2.));
                       }
                                                                                                                                          

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;

int K=200,K1=K+1;
DB A=10.;  DB dy=2*A/K;  printf("dy=%6.3f",dy);
#define Y(k) (dy*(k-K/2))
printf("y_0=%6.3f y_K=%6.3f ",Y(0), Y(K));
int M=300,M1=M+1;
int N=300,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
FILE *o;o=fopen("TetrationBaseSqrt2v01a.eps","w");
ado(o,0,0,214,212);
fprintf(o,"112 110 translate\n 10 10 scale\n");
DB sy=10./(N/2.);
DO(m,M1) X[m]=-11+.07*m;
DO(n,N1) Y[n]=sy*(n-N/2.+.5);
for(m=-10;m<11;m++) {M(m,-10)L(m,10)}
for(n=-10;n<11;n++) {M(  -10,n)L(10,n)} fprintf(o,".006 W 0 0 0 RGB S\n");
fprintf(o,"/adobe-Roman findfont 1 scalefont setfont\n");
for(m=-8;m<0;m+=2) {M(-11.2,m-.3) fprintf(o,"(%1d)s\n",m);}
for(m= 0;m<9;m+=2) {M(-10.7,m-.3) fprintf(o,"(%1d)s\n",m);}
for(m=-8;m<0;m+=4) {M(m-.6,-10.8) fprintf(o,"(%1d)s\n",m);}
for(m= 0;m<9;m+=4) {M(m-.3,-10.8) fprintf(o,"(%1d)s\n",m);}
fprintf(o,"/Times-Italic findfont 1 scalefont setfont\n");
//fprintf(o,"/adobe-italic findfont 1 scalefont setfont\n");
M(  9.6,-10.8) fprintf(o,"(y)s\n");
M(-10.7,  9.5) fprintf(o,"(x)s\n");
M(-11,0)L(10.1,0) M(0,-11)L(0,10.1) fprintf(o,".01 W 1 0 1 RGB S\n");
z_type tm,tp,F[M1*N1];;


DO(m,M1)DO(n,N1){      g[m*N1+n]=9999;
                       f[m*N1+n]=9999;}
for(m=0;m<M1;m++){     x=X[m]; int m1;
                       DO(n,N1){y=Y[n]; z=z_type(x,y);
                               // c=sqrt2a(z)-log(sqrt2a(z+1.))/log(sqrt(2.));
                               c=sqrt2b(z);
                               p=Re(c);
                               q=Im(c);
                               if(p>-9999 && p<9999) g[m*N1+n]=p;
                               if(q>-9999 && q<9999) f[m*N1+n]=q;
                               }
               }
p=.8;
                  conto(o,f,w,v,X,Y,M,N, (-5.     ), -1,1); fprintf(o,".06 W 1 0 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (-4.     ), -2,2); fprintf(o,".06 W 1 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-4.+.1*n),-.3,.3);fprintf(o,".01 W 0 1 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (-3.     ), -p,p); fprintf(o,".06 W 1 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-3.+.1*n),-.3,.3);fprintf(o,".01 W 0 1 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (-2.     ), -2,2); fprintf(o,".06 W 1 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-2.+.1*n),-.3,.3);fprintf(o,".01 W 0 1 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (-1.     ), -p,p); fprintf(o,".06 W 1 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-1.+.1*n),-.1,.1);fprintf(o,".01 W 0 1 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (0.      ), -p,p); fprintf(o,".06 W 0 .8 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 0+ .1*n),-.1,.1);fprintf(o,".01 W 0 1 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 1.     ), -p,p); fprintf(o,".06 W 0 0 1 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 1.+.1*n),-.3,.3);fprintf(o,".01 W 0 1 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 2.     ), -2,2); fprintf(o,".06 W 0 0 1 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 2.+.1*n),-.3,.3); fprintf(o,".01 W 0 1 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 3.     ), -2,2); fprintf(o,".06 W 0 0 1 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 3.+.1*n),-.3,.3);fprintf(o,".01 W 0 1 0 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 4.     ), -2,2); fprintf(o,".06 W 0 0 1 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, ( 5.     ), -1,1); fprintf(o,".06 W 0 0 1 RGB S\n");
                                                                                                                                          
                  conto(o,g,w,v,X,Y,M,N, (-2.     ),-3,3); fprintf(o,".06 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-2.+.1*n),-p,p); fprintf(o,".01 W 1 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, (-1.     ),-3,3); fprintf(o,".06 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-1.+.1*n),-p,p); fprintf(o,".01 W 1 0 0 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, (0.      ),-3,3); fprintf(o,".06 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (    .1*n),-p,p); fprintf(o,".01 W 0 0 1 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 1.     ),-3,3); fprintf(o,".06 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 1.+.1*n),-p,p); fprintf(o,".01 W 0 0 1 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 2.     ),-3,3); fprintf(o,".06 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 2.+.1*n),-p,p); fprintf(o,".01 W 0 0 1 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 3.     ),-3,3); fprintf(o,".06 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 3.+.1*n),-p,p); fprintf(o,".01 W 0 0 1 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 4.     ),-3,3); fprintf(o,".06 W 0 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 4.+.1*n),-p,p); fprintf(o,".01 W 0 0 1 RGB S\n");
                  conto(o,g,w,v,X,Y,M,N, ( 5.     ),-2,2); fprintf(o,".06 W 0 0 0 RGB S\n");
z=1.e-16;
printf("%18.16f \n", Re(sqrt2b(-z)));
printf("%18.16f \n", Re(sqrt2b( z)));

//M(-10,0)L(-2,0)fprintf(o,".04 W 1 0 1 RGB S\n");

fprintf(o,"showpage\n\%\%\%Trailer"); fclose(o);
       system( "ggv TetrationBaseSqrt2v01a.eps &"); //for UNIX
//     system("open TetrationBaseSqrt2v01a.eps"); //for macintosh
system("nice ps2pdf TetrationBaseSqrt2v01a.eps");
//getchar(); system("killall Preview"); // For macintosh

}

// end of TetrationBaseSqrt2v01.cc //